Highest Common Factor of 505, 1700 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 505, 1700 i.e. 5 the largest integer that leaves a remainder zero for all numbers.
HCF of 505, 1700 is 5 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 505, 1700 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 505, 1700 is 5.
HCF(505, 1700) = 5
HCF of 505, 1700 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 505, 1700 is 5.
Highest Common Factor of 505,1700 is 5
Step 1: Since 1700 > 505, we apply the division lemma to 1700 and 505, to get
1700 = 505 x 3 + 185
Step 2: Since the reminder 505 ≠ 0, we apply division lemma to 185 and 505, to get
505 = 185 x 2 + 135
Step 3: We consider the new divisor 185 and the new remainder 135, and apply the division lemma to get
185 = 135 x 1 + 50
We consider the new divisor 135 and the new remainder 50,and apply the division lemma to get
135 = 50 x 2 + 35
We consider the new divisor 50 and the new remainder 35,and apply the division lemma to get
50 = 35 x 1 + 15
We consider the new divisor 35 and the new remainder 15,and apply the division lemma to get
35 = 15 x 2 + 5
We consider the new divisor 15 and the new remainder 5,and apply the division lemma to get
15 = 5 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 505 and 1700 is 5
Notice that 5 = HCF(15,5) = HCF(35,15) = HCF(50,35) = HCF(135,50) = HCF(185,135) = HCF(505,185) = HCF(1700,505) .
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Frequently Asked Questions on HCF of 505, 1700 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 505, 1700?
Answer: HCF of 505, 1700 is 5 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 505, 1700 using Euclid's Algorithm?
Answer: For arbitrary numbers 505, 1700 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
